CN112507479B - Oil drilling machine health state assessment method based on manifold learning and softmax - Google Patents

Oil drilling machine health state assessment method based on manifold learning and softmax Download PDF

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CN112507479B
CN112507479B CN202011299670.XA CN202011299670A CN112507479B CN 112507479 B CN112507479 B CN 112507479B CN 202011299670 A CN202011299670 A CN 202011299670A CN 112507479 B CN112507479 B CN 112507479B
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CN112507479A (en
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李波
邓慧敏
胡家文
洪涛
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University of Electronic Science and Technology of China
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Abstract

The invention provides a petroleum drilling machine health state assessment method based on manifold learning and softmax, and belongs to the field of equipment data analysis. Firstly, standardizing a vibration signal and extracting characteristics; and then carrying out dimensionality reduction based on manifold learning on the high-dimensional vibration signal characteristics to obtain a low-dimensional space characteristic vector, carrying out softmax model training on the low-dimensional vector to obtain a classification result, calculating the Mahalanobis distance between an output result sequence and a health sequence, converting the Mahalanobis distance into a health index, and carrying out quantitative expression on the health index to realize the health state evaluation of the oil drilling machine system. According to the method, the intrinsic dimension based on the maximum likelihood estimation is subjected to self-adaptive weighting, the contribution of a data point is corrected, meanwhile, a distance measurement formula is improved by utilizing label information, the aliasing degree among different categories is reduced, meanwhile, the health state of the oil drilling machine is evaluated by combining the Mahalanobis distance, the accuracy and the stability of an evaluation result are improved, and powerful support is provided for the fault prediction and maintenance of the oil drilling machine.

Description

Oil drilling machine health state assessment method based on manifold learning and softmax
Technical Field
The invention belongs to the technical field of equipment health management, and relates to a method for health assessment of key mechanical equipment of an oil drilling machine, in particular to an oil drilling machine health state assessment method based on manifold learning and a softmax classifier.
Background
The concept of health assessment was first derived from human health management and then gradually introduced into the scientific management of complex equipment, the first being applied to aeroengine management. The health state can be qualitatively described as whether the equipment can complete a given task, and quantitatively described as the performance difference between the current state and the initial service stage of the equipment, or the distance between the current state and the failure state of the equipment.
The currently common method for assessing the health status of equipment is driven by physical models and data. Due to the complexity of the structure of the complex equipment, an accurate mechanism model is difficult to establish, the data-driven method has the advantage of complex system modeling, and a large amount of operation data is reserved due to the establishment of various monitoring systems, so that the data-driven health assessment method is widely concerned.
The method mainly comprises three types of complex equipment health assessment methods based on data driving, wherein one type of the complex equipment health assessment method is a health assessment method taking state characteristic distance measurement as a core, the other type of the complex equipment health assessment method is a health assessment method based on a statistical theory to carry out health state estimation, and the third type of the complex equipment health assessment method is a reliability modeling method based on a reliability theory to carry out reliability modeling according to a complex equipment physical structure so as to estimate the overall health level.
The data driving method has the problems of complex calculation process, insensitivity to health state and the like, an oil drilling machine system belongs to large-scale complex equipment, the composition relation is complex, and visual oil drilling machine health state evaluation research is not available in China at present, so technical personnel in the field are dedicated to research on the health state evaluation method for oil drilling machine equipment, the abnormity of main mechanical equipment is analyzed, the drilling machine is monitored in time before an accident occurs, and a foundation is laid for equipment maintenance.
Disclosure of Invention
The invention aims to provide an oil rig health state assessment method based on manifold learning and softmax aiming at the characteristics of nonlinearity and instability of a vibration signal of an oil rig, so that the defects in the background technology are overcome, and the health state of the oil rig is assessed by combining the manifold learning and state recognition, so that the accuracy of assessment results is improved.
The invention relates to an oil rig health state assessment method based on manifold learning and softmax, which comprises the following steps of:
step 1: collecting vibration signals of N different measuring points of the petroleum drilling machine system equipment under different health states,
Figure BDA0002786442320000011
j is 1,2, … …, m is sample length, the vibration signal is normalized by mean-variance and divided into training set S1 and testing set S2;
step 2: the normalized vibration signal has zero mean and unit variance, and time domain features and frequency domain features are respectively extracted from the normalized vibration signal on the basis of time domain and frequency domain;
then the time domain feature vector alphai,lSum frequency domain feature vector betai,lComprises the following steps:
αi,l＝[αi,l,1,αi,l,2,...,αi,l,t]
βi,l＝[βi,l,1,βi,l,2,...,βi,l,f]
wherein alpha isi,l,tThe t-th time-domain characteristic parameter, beta, of the i-th sample in the healthy state li,l,fThe method comprises the steps that f frequency domain characteristic parameters of an ith sample in a healthy state l are represented, wherein i represents that the ith sample in the healthy state l is 1, t, n and f are the total number of samples, t is the number of time domain characteristic parameters, and f is the number of the frequency domain characteristic parameters;
and step 3: constructing a high-dimensional characteristic matrix for vibration signal samples in different health states at different measuring point positions, and arranging time domain characteristic vectors and frequency domain characteristic vectors of original vibration signals in sequence to form a high-dimensional characteristic vector of the ith sample:
Si＝[αi,0,αi,1,αi,2,…,αi,t,βi,0,βi,1,βi,2,…,βi,f]T
and then, a high-dimensional feature matrix of each state is formed:
Figure BDA0002786442320000023
wherein N islSampling a vibration signal of the oil rig system in a healthy state I;
and 4, step 4: extracting low-dimensional embedded components, reducing the dimensions of the high-dimensional characteristic matrix of the vibration signals with different health states constructed in the step (3), and representing the health state of the oil drilling machine system;
step 4.1: calculating sample points x in different health statesiFor each point in the high-dimensional eigenspace, x is determinediK nearest neighbor points of (2)i＝[xi1,xi2,…,xik]And selecting according to the optimal classification effect.
Step 4.2: calculating d eigenvectors mapped by the global coordinate by k local nearest neighbors by utilizing maximum likelihood estimation; using a neighbor number k as a sphere radius, obtaining local dimension maximum likelihood estimation, and obtaining a global intrinsic dimension by taking an average value of the intrinsic dimensions of each sample point; the local dimension maximum likelihood estimate is:
Figure BDA0002786442320000021
wherein T isk(xi) Is xiEuclidean distance to its k-th neighbor;
step 4.3: and (3) simplifying the dimension of the original high-dimensional feature vector by selecting the number k of the adjacent points and calculating the intrinsic dimension to obtain a low-dimensional feature vector set in different health states:
Figure BDA0002786442320000022
wherein
Figure BDA0002786442320000031
d is the dimension of the feature vector after the dimension reduction;
and 5: inputting the low-dimensional characteristic vector after the training sample is reduced into a softmax model for training to obtain the probability that the sample belongs to different health states;
training a softmax classifier by using the low-dimensional feature vectors under different health state labels in the step 4, wherein the output of the classifier is a first-order probability matrix which represents the probability that the sample belongs to different health states; the assumed function is:
Figure BDA0002786442320000032
wherein, p (y)(i)＝l∣x(i)(ii) a θ) represents a sample x(i)Probability of belonging to class j, y(i)Label, x, representing the ith sample(i)Denotes the ith training sample, θlFor the model parameter vector, the cost function of θ is defined as:
J(θ)＝J(θ(1))+J(θ(2))+…+J(θ(K))
J(θ(k)) Is defined as:
Figure BDA0002786442320000033
step 6: inputting the test samples after dimensionality reduction according to the iteration times and the model parameter requirements set in the softmax model in the step 5, outputting the probability that each test sample belongs to different health state grades, and taking the health state corresponding to the result of the maximum test sample membership probability as the final health state grade;
and 7: and calculating the Mahalanobis distance between the final health state grade sequence and the health state sequence of the oil drilling machine system, and calculating the range of the health indexes under different health state grades.
Further, in the step 1, according to the performance degradation process of the oil drilling rig system, different health states of the oil drilling rig system are divided into 5 grades, namely health, good, qualified, abnormal and fault states; vibration signals in 5 states were collected for each station position.
Further, the time domain features in step 2 are 13 time domain features of the vibration signal, and include: absolute mean, maximum peak, root mean square value, square root amplitude, variance, peak-to-peak, kurtosis, skewness, peak index, waveform index, pulse index, margin index, kurtosis index; the frequency domain features are 7 time domain features of the vibration signal, and comprise: average frequency, spectral peak stability index, first band relative energy, second channel relative energy, third band relative energy, fourth band relative energy, and fifth band relative energy.
Further, the improved distance d combining the euclidean distance and the cosine similarity is adopted in the step 4.1ijThe measurement mode of (2) selects the neighborhood points, and increases the possibility that the samples with the same health state are selected as the neighborhood points;
Figure BDA0002786442320000041
wherein
Figure BDA00027864423200000410
Are respectively xjAnd xiArtificially determining k values in a neighborhood formed by k nearest neighbor near points according to the optimal classification effect value;
therefore, the neighbor distance matrix is defined as:
Figure BDA0002786442320000042
wherein
Figure BDA0002786442320000043
To improve the distance dijThe distance under the same health state is:
Figure BDA0002786442320000044
the distances under different health conditions were:
Figure BDA0002786442320000045
Figure BDA0002786442320000046
to improve the distance dijAverage value of (a).
Further, said step 4.2 weights the modified intrinsic dimensions taking into account the relationship between each data point and its neighbors; point xiThe weight of (d) can be expressed as:
Figure BDA0002786442320000047
wherein D iskIs a neighbor distance matrix, Ak(xi) Is a point xiDistance to nearest neighbor;
the weighted eigen dimensions are:
Figure BDA0002786442320000048
wherein the content of the first and second substances,
Figure BDA0002786442320000049
represents the local dimension maximum likelihood estimate obtained with the nearest neighbor k:
Figure BDA0002786442320000051
Tk(xi) Is the sample point xiEuclidean distance to its k-th neighbor.
Further, the model parameters in the step 5 are optimized by using an iterative optimization algorithm to a cost function;
for J (theta)(k)) Adding a weight decay term:
Figure BDA0002786442320000052
where λ is a parameter of the model, determined experimentally, C represents a class label,
Figure BDA0002786442320000053
is an n-dimensional real number vector, is a model parameter derived from a training set, liThe label representing the ith sample.
For cost function J (theta)(k)) And solving a partial derivative to obtain a gradient formula:
Figure BDA0002786442320000054
where λ is the parameter of the model, determined experimentally, p (l)i＝j∣xiθ) represents the input training sample of the classifier as xiWhen the output class is liThe probability of (c).
In each iteration of the gradient descent, the following updates are made:
Figure BDA0002786442320000055
further, the health index in step 7 is defined as:
Figure BDA0002786442320000056
wherein MD1Mahalanobis distance, MD, between the health state sequence and the ideal state sequence of the oil rig system2The mahalanobis distance between the health state sequence of the oil drilling machine system and each health state grade sequence.
The evaluation method realizes the grade division and the evaluation of the health state of the oil drilling machine by analyzing the vibration signals of each measuring point of the system of the oil drilling machine, extracting the characteristics and reducing the dimension and combining the softmax classifier to recognize the state.
The manifold learning can carry out dimensionality reduction under the condition of keeping a better original characteristic manifold structure, reduces the pressure of state identification, improves the identification precision of a health state, and an LTSA (low-resolution SA) algorithm provides a main manifold reconstruction display expression from a low-dimensional manifold to a high-dimensional manifold, so that the small mapping change error is ensured, but class label information cannot be utilized, the low-dimensional characteristic sets of different classes possibly have aliasing phenomenon, and the problem of uncertainty of artificial setting of intrinsic dimensions exists. The method carries out self-adaptive weighting on the intrinsic dimension based on the maximum likelihood estimation, considers the relationship between each data point and the adjacent points thereof, corrects the contribution of the data points, simultaneously utilizes the label information, improves the distance measurement formula, reduces the aliasing degree among different categories, improves the accuracy and the stability of the health state estimation, and has practical significance.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a flow chart of an oil rig state of health assessment method based on manifold learning and softmax of the present invention.
Detailed Description
The invention will be described in further detail below with reference to the drawings, which are intended to illustrate the invention and not to limit it.
The problems of the invention are solved by the following technical scheme:
based on historical operation data of vibration signals of each measuring point of an oil drilling machine system and health state classification under performance degradation, firstly, the vibration signals are subjected to standardization processing, and characteristics are extracted. And then carrying out dimensionality reduction based on manifold learning on the high-dimensional vibration signal characteristics to obtain a low-dimensional space characteristic vector, carrying out softmax model training on the low-dimensional vector to obtain a classification result, calculating the Mahalanobis distance between an output result sequence and a health sequence, converting the Mahalanobis distance into a health index, and carrying out quantitative expression on the health index to realize the health state evaluation of the oil drilling machine system.
The method for evaluating the health state of the oil drilling machine comprises the following steps:
step 1: collecting vibration signals of N different measuring points of a certain system device of the oil drilling rig under different health states,
Figure BDA0002786442320000061
j is 1,2, … …, m, m is the sample length, the vibration signal is mean-variance normalized and divided into two data subsets S1, S2 for training and testing. According to the performance degradation process of the oil drilling machine system, different health states of the oil drilling machine system are divided into 5 grades, namely health, good, qualified, abnormal and fault states. Vibration signals in 5 states were collected for each station position, as shown in table 2.
Table 2 is a petroleum drilling machine health status grade division description table
Figure BDA0002786442320000062
Figure BDA0002786442320000071
Step 2: the normalized vibration signal has zero mean and unit variance, and time domain original features and frequency domain features are extracted from the normalized vibration signal based on time domain and frequency domain analysis.
The time domain feature vector and the frequency domain feature vector are respectively:
αi,l＝[αi,l,1,αi,l,2,...,αi,l,t]
βi,l＝[βi,l,1,βi,l,2,...,βi,l,f]
where i denotes the ith sample i in the healthy state l, which is 1., n, t is the number of time domain feature parameters, and f is the number of frequency domain feature parameters.
The time domain features are 13 time domain features of the vibration signal, including an absolute mean, a maximum peak, a root mean square value, a root mean square amplitude, a variance, a peak-to-peak value, a kurtosis, a skewness, a peak index, a waveform index, a pulse index, a margin index and a kurtosis index. The frequency domain features are 7 time domain features of the vibration signal, including an average frequency, a spectral peak stability index, a first frequency band relative energy, a second channel relative energy, a third frequency band relative energy, a fourth frequency band relative energy, and a fifth frequency band relative energy.
And step 3: constructing a high-dimensional characteristic matrix for vibration signal samples in different health states at different measuring point positions, and arranging time domain characteristic parameters and frequency domain characteristic parameters of an original vibration signal in sequence to form a high-dimensional characteristic vector of the ith sample:
Si＝[αi,0,αi,1,αi,2,…,αi,t,βi,0,βi,1,βi,2,…,βi,f]T
constructing a high-dimensional feature matrix for each state:
SNl＝[s1,s2,…,sNl]T
wherein N islIs a sample of the oil rig system vibration signal in healthy state i.
And 4, step 4: and (3) extracting a low-dimensional embedded component by utilizing an LTSA manifold algorithm, reducing the dimension of the high-dimensional characteristic matrix of the vibration signals with different health states constructed in the step (3), and further representing the health state of a certain system of the oil drilling rig.
Step 4.1: selecting neighborhood, calculating each sample point x in different health statesiFor each point in the high-dimensional eigenspace, x is determinediK nearest neighbors ofNeighborhood of points Xi＝[xi1,xi2,…,xik]。
And selecting the neighborhood points by adopting an improved distance measurement mode of combining Euclidean distance and cosine similarity, and increasing the possibility that samples with the same health state are selected as the neighborhood points.
Figure BDA0002786442320000081
Wherein
Figure BDA0002786442320000082
Are respectively xjAnd xiThe cosine similarity and the euclidean distance.
Defining the distance under the same health condition as
Figure BDA0002786442320000083
The distance under different health conditions is
Figure BDA0002786442320000084
Wherein
Figure BDA0002786442320000085
Is xiMean of improved distances from the neighborhood.
Step 4.2: using maximum likelihood estimation, d eigenvectors of the global coordinate map are computed from k local nearest neighbors. And (3) using the nearest neighbor number k as the radius of the sphere to obtain local dimension maximum likelihood estimation, and taking the average value of the intrinsic dimensions of each sample point to obtain the global intrinsic dimension. The local dimension maximum likelihood estimate is:
Figure BDA0002786442320000086
wherein T isk(xi) Is xiEuclidean distance to its k-th neighbor.
The eigen-dimensions are weighted and modified taking into account the relationship between each data point and its neighbors. Point xiCan be expressed as
Figure BDA0002786442320000087
Wherein DkIs a neighbor distance matrix, Ak(xi) Is a point xiDistance to nearest neighbor
The weighted eigen dimensions are:
Figure BDA0002786442320000088
step 4.3: and (3) carrying out dimensionality reduction on the original high-dimensional feature vector through an LTSA algorithm by selecting the number k of adjacent points and calculating the intrinsic dimensionality to obtain a low-dimensional vector set in different health states:
Figure BDA0002786442320000091
wherein
Figure BDA0002786442320000092
d is the dimension of the feature vector after the dimension reduction.
And 5: inputting the low-dimensional feature vector after the training sample is reduced into a softmax model for training, and obtaining the probability that the sample belongs to different health states.
And (4) training a softmax classifier by using the low-dimensional vectors under different health state labels in the step (4), wherein the output of the classifier is a first-order probability matrix which represents the probability that the sample belongs to different health states. The assumed function is:
Figure BDA0002786442320000093
where θ is the model parameter. The cost function for θ is defined as:
J(θ)＝J(θ(1))+J(θ(2))+…+J(θ(K))
J(θ(k)) Is defined as:
Figure BDA0002786442320000094
the model parameters are optimized for the cost function using an iterative optimization algorithm.
For J (theta)(k)) Adding a weight decay term:
Figure BDA0002786442320000095
where λ is the parameter of the model, determined experimentally.
For cost function J (theta)(k)) And solving a partial derivative to obtain a gradient formula:
Figure BDA0002786442320000096
in each iteration of the gradient descent, the following updates are made:
Figure BDA0002786442320000101
step 6: inputting the test samples after dimensionality reduction according to the iteration times and the model parameter requirements set in the softmax model in the step 5, outputting the probability that each test sample belongs to different health state grades, and taking the health state corresponding to the result of the maximum test sample membership probability as the final health state grade.
And 7: and calculating the Mahalanobis distance between the final health state grade sequence and the health state sequence of the oil drilling machine system, and calculating the range of the health indexes under different health state grades.
The health index is defined as:
Figure BDA0002786442320000102
wherein MD1Mahalanobis distance, MD, between the oil rig system state sequence and the ideal state sequence2The mahalanobis distance between the system state sequence of the oil drilling machine and each health state grade sequence.

Claims (7)

1. A method for evaluating the health status of an oil drilling machine based on manifold learning and softmax, which comprises the following steps:
step 1: collecting vibration signals of N different measuring points of the petroleum drilling machine system equipment under different health states,
Figure FDA0002786442310000011
m is the sample length, the vibration signal is subjected to mean-variance standardization and is divided into a training set S1 and a testing set S2;
step 2: the normalized vibration signal has zero mean and unit variance, and time domain features and frequency domain features are respectively extracted from the normalized vibration signal on the basis of time domain and frequency domain;
then the time domain feature vector alphai,lSum frequency domain feature vector betai,lComprises the following steps:
αi,l＝[αi,l,1,αi,l,2,...,αi,l,t]
βi,l＝[βi,l,1,βi,l,2,...,βi,l,f]
wherein alpha isi,l,tThe t-th time-domain characteristic parameter, beta, of the i-th sample in the healthy state li,l,fThe method comprises the steps that f frequency domain characteristic parameters of an ith sample in a healthy state l are represented, wherein i represents that the ith sample in the healthy state l is 1, t, n and f are the total number of samples, t is the number of time domain characteristic parameters, and f is the number of the frequency domain characteristic parameters;
and step 3: constructing a high-dimensional characteristic matrix for vibration signal samples in different health states at different measuring point positions, and arranging time domain characteristic vectors and frequency domain characteristic vectors of original vibration signals in sequence to form a high-dimensional characteristic vector of the ith sample:
Si＝[αi,0,αi,1,αi,2,…,αi,t,βi,0,βi,1,βi,2,…,βi,f]T
and then, a high-dimensional feature matrix of each state is formed:
Figure FDA0002786442310000012
wherein N islSampling a vibration signal of the oil rig system in a healthy state I;
and 4, step 4: extracting low-dimensional embedded components, reducing the dimensions of the high-dimensional characteristic matrix of the vibration signals with different health states constructed in the step (3), and representing the health state of the oil drilling machine system;
step 4.1: calculating sample points x in different health statesiFor each point in the high-dimensional eigenspace, x is determinediK nearest neighbor points of (2)i＝[xi1,xi2,…,xik]Selecting according to the optimal classification effect;
step 4.2: calculating d eigenvectors mapped by the global coordinate by k local nearest neighbors by utilizing maximum likelihood estimation; using a neighbor number k as a sphere radius, obtaining local dimension maximum likelihood estimation, and obtaining a global intrinsic dimension by taking an average value of the intrinsic dimensions of each sample point; the local dimension maximum likelihood estimate is:
Figure FDA0002786442310000021
wherein T isk(xi) Is xiEuclidean distance to its k-th neighbor;
step 4.3: and (3) simplifying the dimension of the original high-dimensional feature vector by selecting the number k of the adjacent points and calculating the intrinsic dimension to obtain a low-dimensional feature vector set in different health states:
Figure FDA0002786442310000022
wherein
Figure FDA0002786442310000023
d is the dimension of the feature vector after the dimension reduction;
and 5: inputting the low-dimensional characteristic vector after the training sample is reduced into a softmax model for training to obtain the probability that the sample belongs to different health states;
training a softmax classifier by using the low-dimensional feature vectors under different health state labels in the step 4, wherein the output of the classifier is a first-order probability matrix which represents the probability that the sample belongs to different health states; the assumed function is:
Figure FDA0002786442310000024
wherein, p (y)(i)＝l∣x(i)(ii) a θ) represents a sample x(i)Probability of belonging to class j, y(i)Label, x, representing the ith sample(i)Denotes the ith training sample, θlFor the model parameter vector, the cost function of θ is defined as:
J(θ)＝J(θ(1))+J(θ(2))+…+J(θ(K))
J(θ(k)) Is defined as:
Figure FDA0002786442310000025
step 6: inputting the test samples after dimensionality reduction according to the iteration times and the model parameter requirements set in the softmax model in the step 5, outputting the probability that each test sample belongs to different health state grades, and taking the health state corresponding to the result of the maximum test sample membership probability as the final health state grade;
and 7: and calculating the Mahalanobis distance between the final health state grade sequence and the health state sequence of the oil drilling machine system, and calculating the range of the health indexes under different health state grades.
2. The method for evaluating the health state of the oil drilling machine based on manifold learning and softmax as claimed in claim 1, wherein in the step 1, the different health states of the oil drilling machine system are divided into 5 grades according to the performance degradation process of the oil drilling machine system, and are healthy, good, qualified, abnormal and fault; vibration signals in 5 states were collected for each station position.
3. The method of claim 1, wherein the time domain features of step 2 are 13 time domain features of a vibration signal, and the method comprises: absolute mean, maximum peak, root mean square value, square root amplitude, variance, peak-to-peak, kurtosis, skewness, peak index, waveform index, pulse index, margin index, kurtosis index; the frequency domain features are 7 time domain features of the vibration signal, and comprise: average frequency, spectral peak stability index, first band relative energy, second channel relative energy, third band relative energy, fourth band relative energy, and fifth band relative energy.
4. The method for evaluating the health of an oil drilling machine based on manifold learning and softmax as claimed in claim 1, wherein the step 4.1 employs the modified distance d of the Euclidean distance combined with the cosine similarityijThe measurement mode of (2) selects the neighborhood points, and increases the possibility that the samples with the same health state are selected as the neighborhood points;
Figure FDA0002786442310000031
wherein
Figure FDA0002786442310000032
Are respectively xjAnd xiArtificially determining k values in a neighborhood formed by k nearest neighbor near points according to the optimal classification effect value;
therefore, the neighbor distance matrix is defined as:
Figure FDA0002786442310000033
wherein
Figure FDA0002786442310000034
To improve the distance dijThe distance under the same health state is:
Figure FDA0002786442310000035
the distances under different health conditions were:
Figure FDA0002786442310000036
Figure FDA0002786442310000037
to improve the distance dijAverage value of (a).
5. A method of oil rig state of health assessment based on manifold learning and softmax as claimed in claim 1, characterized in that said step 4.2 weights the modified intrinsic dimension taking into account the relation between each data point and its neighbours; point xiThe weight of (d) can be expressed as:
Figure FDA0002786442310000041
wherein D iskIs a neighbor distance matrix, Ak(xi) Is a point xiDistance to nearest neighbor;
the weighted eigen dimensions are:
Figure FDA0002786442310000042
wherein the content of the first and second substances,
Figure FDA0002786442310000043
represents the local dimension maximum likelihood estimate obtained with the nearest neighbor k:
Figure FDA0002786442310000044
Tk(xi) Is the sample point xiEuclidean distance to its k-th neighbor.
6. The method for evaluating the health of an oil drilling rig based on manifold learning and softmax as claimed in claim 1, wherein the model parameters in the step 5 are optimized for the cost function using an iterative optimization algorithm;
for J (theta)(k)) Adding a weight decay term:
Figure FDA0002786442310000045
where λ is a parameter of the model, determined experimentally, C represents a class label,
Figure FDA0002786442310000046
is an n-dimensional real number vector, is a model parameter derived from a training set, liA label representing the ith sample;
to costFunction J (theta)(k)) And solving a partial derivative to obtain a gradient formula:
Figure FDA0002786442310000047
where λ is the parameter of the model, determined experimentally, p (l)i＝j∣xiθ) represents the input training sample of the classifier as xiWhen the output class is liThe probability of (d);
in each iteration of the gradient descent, the following updates are made:
Figure FDA0002786442310000051
7. the method of claim 1, wherein the health index in step 7 is defined as:
Figure FDA0002786442310000052
wherein MD1Mahalanobis distance, MD, between the health state sequence and the ideal state sequence of the oil rig system2The mahalanobis distance between the health state sequence of the oil drilling machine system and each health state grade sequence.
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